Hi there and thank you for your question,
The short story is that the Consumer Protection Act won't apply to you as the "consumer" in your situation was the school, and not a person in his private capacity.
At the end of the day the answer unfortunately rests in the contract. If the contract says a fixed term of 60 months, then that is the answer and they can't claim a 3 month notice period.
If however the contract says that the 60 month period will continue to run month by month, until such time as you give them the 3 months' notice - then unfortunately that is what you've agreed.
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Good luck and best regards,
Please note: This answer does not create an attorney-client relationship. Please consult a local attorney in person for legal advice. This information is being provided so you can better discuss legal matters with your attorney.